Task $2\mathrm{.}1$

Let the signal

$x(t)=sin(2ft)$

with

$f=5Hz$

Write Matlab programs.

a$)$ Sample the signal $x(t).$ The sampling frequency is $f_s=50Hz.$ Plot the sampled signal in the

timeframe $-10t10(t$ in seconds$).$ Use correct axis labels and scaling.

b$)$ Cut out a time frame from $x(t)$ in the range $-5t5.$ Use a rectangular time window $(=1$ for $-5$

$t5$;$=0$ elsewhere$).$ Hint: multiply the rectangular time window pointwise with the sampled

signal. Plot the result from $-10$ to $+10.$ Use correct axis labels and scaling.

c$)$ Calculate the FFT of the cut$-$out time frame $($hint: $500$ sampling points$)$ and plot it$.$ Use correct axis

labels and scaling.

d$)$ Once again cut out a time frame from $x(t)$ in the range $-5t5.$ This time use a Hamming window.

Hint: Create a Hamming window using the corresponding Matlab function. Use the same sampling rate

that you used for sampling $x(t).$

e$)$ Calculate the FFT of the cut$-$out time frame of part d$).$ Use correct axis labels and scaling.

Now please answer the next question without using Matlab

f$)$ Compare the FFTs of c$)$ and e$)$ and discuss the differences.

Submit the solutions: Matlab source code in $.$m files $($no copies or scans$),$ printed plots, and written answers.